Hi Paul,
If you're looking for packaged solvers, then PETSc (already mentioned)
and Aztec could be of interest to you. Aztec is a parallel iterative
solver for sparse systems developed by Sandia Labs.
(Aztec: http://www.cs.sandia.gov/CRF/aztec1.html )
There is also a direct solver for symmetric positive definite matrices
called PSPASES (http://www-users.cs.umn.edu/~mjoshi/pspases/), but I
haven't ever looked at that myself, so I can't really tell you much
about it.
Another direct solution package, originally written for the RS6000
platform but now available for linux (I believe!), is the Watson Sparse
Matrix Package (WSMP) (http://www-users.cs.umn.edu/~agupta/wsmp.html),
by Anshul Gupta. Not only is the package said to be very good, but
Gupta has done a LOT of research on sparse matrices, and it couldn't
hurt to read some of his publications.
On a different note, if you're not looking for packaged solvers, and
just want to know about various methods or want to implement your own
-often faster, if you have a known structure in your matrix-, you might
want to read up on Yousef Saad's work, as mentioned before. Also, a
very useful (and thick!) book is Golub and Van Loan's "Matrix
Computations". Finally, if you find you're having difficulty with
getting decent preconditioners (if necessary), I'd also suggest taking a
look at Michele Benzi's work on sparse approximate inverse
preconditioners. (http://www.mathcs.emory.edu/~benzi/)
(That last link also has links to other people/places doing research
that may be of interest to you.)
Hope some of that is of interest to you,
- Brian
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